Diagonalizing the above Hamiltonian (REF ), we obtain the
quasiparticle energy spectrum \( E({\bf k})=2st\sqrt{\cos ^2(k_xl)+\cos ^2(k_zl)} \)  with \(s=\pm 1\)  being the band
index, which is similar to the spectrum of \(\pi \)  flux states in
quantum spin liquids [1]}. This energy spectrum has two energy
bands and
contains four zero-energy
Dirac points, where the conduction and
valence bands intersect, in the first Brillouin zone at \( {\bf K}_1=\left({\pi }/{2l},{\pi }/{2l}\right), {\bf K}_2=\left(-{\pi }/{2l},{\pi }/{2l}\right), {\bf K}_3=\left({-\pi }/{2l},-{\pi }{2l}\right), {\bf K}_4=\left({\pi }/{2l},-{\pi }/{2l}\right)\) . Near the Dirac points,
the energy dispersion has standard cone-like shape as shown in
Fig.REF  (a) and (b) and the spectrum is linear. The
low-energy state dynamics are described by
linearizing their spectrum about the degeneracy points and are
modeled by massless relativistic fermions.
